Locating transition states on potential energy surfaces by the gentlest ascent dynamics

2015

Int. J. Quantum Chem.

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The ring opening of cyclobutene is characterized by a competition of the two different pathways: a usual pathway over a saddle of index one (SP 1 ) along the conrotatory behavior of the end groups, as well as a "forbidden" pathway over a saddle point of index two (SP 2 ) along the disrotatory behavior of the end CH 2 groups. We use the system of ordinary differential equations for the method of the gentlest ascent dynamics (GAD) to determine saddle points of the potential energy surface (PES) of the ring opening of cyclobutene to cis-butadiene. We apply generalized GAD formulas for the search of a saddle point of index two. To understand the relation of the different regions of the PES (around minimums, around SPs of index one or two) we also calculate valley-ridge inflection (VRI) points on the PES using Newton trajectories (NT). VRIs and the corresponding singular NTs subdivide the regions of "attraction" of the different SPs. We calculate the connections of the SP 2 (in its different symmetry versions) with different SPs of index one of the PES by different "reaction pathways." We compare the possibilities of the tool of the GAD curves for the exploration of PESs with these of NT. The barrier of the disrotatory SP 2 is somewhat higher than the barrier of the conrotatory SP 1 , however, pathways across the slope to the SP 2 open additional reaction valleys. IntroductionMathematics has had a profound impact on science, providing a means to understand the world around us in unprecedented ways.[1] With the advantage of the computer age, the subject of modelization has hugely grown in importance. In particular, over the last decades significant advances in our understanding of the world of chemistry have culminated in the development of a very large set of concepts. Some of these concepts are the potential energy surface (PES) [2][3][4] and the chemical reaction path (RP) [5] being the basic concepts for the theories of chemical dynamics and chemical transformations. The PES is a continuous function of the coordinates of the nuclei over an IR N , thus it is an N-dimensional hypersurface. It should have continuous derivatives of at least second order for our treatments. If Cartesian coordinates are used, then N53 n, however, we may also use N53 n26 nonredundant, internal coordinates for an n-atomic molecule. The PES can be seen as formally divided in catchments associated with local minima.[2] For such a picture, one has in mind steepest descent (SD) curves. The first order saddle points or transition states (TSs) are located at the deepest points of the boundary of the basins. TSs and minima correspond to stationary points of the PES. Two adjacent minima of the PES can be connected through a TS via a continuous curve in the N-dimensional coordinate space, describing the coordinates of the nuclei. The curve characterizes a RP. The concept of the RP has found a widespread use in descriptions of reaction mechanisms, which are based on geometrical rearrangements of the atoms comprising a given chemical system. [6] Mor...

Section: Discussionmentioning

confidence: 99%

“…[22,31]. The performance of such methods is very good and they converge as fast as possible to a correct solution.…”

Section: Numerical Methods and Computational Detailsmentioning

confidence: 97%

Section: Review On the Gad And Newton Trajectory Pathwaysmentioning

confidence: 99%

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Embedding of the saddle point of index two on the PES of the ring opening of cyclobutene

2015

Int. J. Quantum Chem.

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“…The properties and features of some RP curves mentioned above are variational in nature, like the steepest descent [13,14], gradient extremals [15], and the distinguished reaction coordinate also known as NT [16]. An attempt to reach the variationality of the GAD curve model is reported in reference [17] based on the concept of the image function. However this result is not general since it is applicable only to quadratic regions of the PES.…”

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confidence: 99%

“…We recall that the set of coupled first order ordinary differential equations, Eqs. 1and 2, constitute the basic expressions of the GAD model [11,17]. In Section II we introduce the variational approach with a Randers metric [22].…”

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confidence: 99%

The variational nature of the gentlest ascent dynamics and the relation of a variational minimum of a curve and the minimum energy path

2015

Theor Chem Acc

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It is shown that the path described by the gentlest ascent dynamics to find transition states [W. E and X. Zhou, Nonlinearity 24, 1831 (2011)] is an example of a quickest nautical path for a given stationary wind or current, the so-called Zermelo navigation variational problem. In the present case the current is the gradient of the potential energy surface. The result opens the possibility to propose new curves based on Zermelo's theory for two tasks: locate transition states and define reaction paths. The relation between a minimal variational character, that some former reaction pathways possess, and the minimum energy path is discussed.

Locating saddle points of any index on potential energy surfaces by the generalized gentlest ascent dynamics

2014

Theor Chem Acc

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The system of ordinary differential equations for the method of the gentlest ascent dynamics (GAD) is tested to determine the saddle points of the potential energy surface of some molecules. The method has been proposed earlier [E W, Zhou X Nonlinearity 24:1831 (2011)]. We additionally use the metric of curvilinear internal coordinates. By a number of examples we explain the possibilities of a GAD curve: it can find the transition state of interest by a gentlest ascent, directly or indirectly, or not. A GAD curve can be a model of a reaction path, if it does not contain a turning point for the energy. We further discuss generalized GAD formulas for the search of saddle points of a higher index. We calculate diverse examples.